A note on the number of maxima in a discrete sample

Yongcheng Qi

Statistics & Probability Letters, 1997, vol. 33, issue 4, 373-377

Abstract: Consider {Xj, j [greater-or-equal, slanted] 1}, a sequence of i.i.d., positive, integer-valued random variables. Let Kn denote the number of the integer j [set membership, variant] {1,2,...,n} for which Xj = max1[less-than-or-equals, slant]m[less-than-or-equals, slant]n Xm. In this paper we prove that limn-->[infinity] EKn = 1 if and only if Kn converges in probability to one, if and only if limn-->[infinity] P(X1=n)/P(X1[greater-or-equal, slanted]n)=0 and prove that Kn converges almost surely to one, if and only if . Some of the results were shown by Baryshnikov et al. (1995) and Brands et al. (1994).

Keywords: Maxima; Almost; sure; convergence (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (4)

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